In this article we will look at the different ways of placing subwoofers in a live sound setup. By subwoofers we mean the loudspeakers that handle the lowest part of the audio spectrum. We often go to a concert and are dismayed to find that the sub signal doesn't reach some spots at the same level as others; that level difference between areas can even seem like a total absence of signal, since our ears work by comparison.
All this explains why reviews of a concert's sound are not all the same, since depending on exactly where audience members are standing, they will form one opinion or another. Comments like "you can't hear the kick," "the bass is buried in the mix," "this brand's system has no low end" or "what a lousy engineer" are very common during and after a concert...
Although we start from the premise that the sound engineer should be aware of how the system sounds throughout the venue, the truth is that sometimes for lack of time, and other times because, fresh out of Academy X, the engineer is just another "star" who never leaves the mixing console, obsessed with the faders, knobs, buttons, LEDs, screens... of the console and the rest of the processors at the FOH (Front Of House) position, the main PA system.
One role that in our country is so far only found at very large companies, although in countries such as England, France, Germany... it is fully established, is that of the "system engineer," who is the one who has to make sure the overall sound for the audience is as even and intelligible as possible.
That way the mix engineer sticks to his job, which is mixing the band that hired him, and the system engineer makes the appropriate adjustments on behalf of the rental company or the tour's production company, and everyone is happy.
*Photo: Louise Stickland. WIcreations
To understand the problems caused by subwoofer placement, we need to understand that a low frequency is omnidirectional, so a single subwoofer reproducing those frequencies will be omnidirectional. The same does not happen when we place two or more sources; this is due to the difference in time with which the audio signals reach each person's ears and to constructive and destructive interference, as the case may be. True, the resulting level of two cabinets would add 6dB, since if we apply the following formula to obtain the resulting SPL when doubling cabinets, 20log 2/1 = 6dB. Sure enough, once the acoustic prediction is done, what we anticipated holds true: the famous "alleys" or "corridors" appear.
So if the engineer never leaves the mix position, he won't notice those alleys. This defect is centered around 100Hz, which is the frequency at which we made the prediction. This strong attenuation, which is nothing other than destructive interference, is called cancellation. Obviously it is not a total cancellation, but we can see that there is a real drop of more than 6 dB across the whole low-frequency spectrum compared with point A; specifically, around 100Hz we have a difference of more than 20dB.
We have already seen that this problem always occurs when we use a left-right subwoofer configuration, that is, in most of the concerts we have attended for years.
So the question is: can this be avoided?
The answer is: Of course it can!
And the follow-up question is: How?
Answer: By applying various theories written in the last century by Harry Olson!!!
These theories can be found in the book "Acoustical Engineering":
2.3 Double Source (pp. 32-35)
2.5 Straight-Line Source (p. 36)
2.6 Beam Tilting by Phase Shifting (pp. 36-37)
2.9 End Fired Line Source (pp. 38-39)
Yes indeed, this is solved by applying the theories Harry Olson wrote in his book Acoustical Engineering, published in 1947. But nobody dared to apply them until a system engineer from our country, specifically ÁLVARO ELENA (MEYER SOUND SPAIN Technical Support), actually started applying them about 4 years ago on tours and at the Benicàssim international festival, winning over with the results the rental company's engineers and the engineers of the Spanish and foreign bands taking part in the festival.
This is a real achievement, since it meant convincing sound engineers of a new concept and idea contrary to what they had believed since the start of their careers. Since then, all these techniques have been applied on the big tours in our country, and the example has spread to the rest of the world, as in the case of the Isle of Wight festival.
Let's look at the techniques and theories that Harry Olson had already explained and that started being applied in Spain before anywhere else.
The theory
Let's see what happens when we place one omnidirectional source at a certain distance from another. If we apply the following formula, we will know the existing phase relationship:
D x Fr x 360/340
If we work with a 90º phase relationship by applying the formula above, the result is summation at the front, where the relationship is 0º, and 90º at the side where we have the greatest difference, that is, a 3dB difference. Doing it with 180º because of the separation distance gives us maximum attenuation at the far side, having separated them by 1.7m, which corresponds to half the wavelength of 100Hz. If we separate the sound sources by 2.27m, the phase relationship is 240º, so we get 6 dB of attenuation relative to the 0º point. Once we reach 240º of separation, cancellation problems appear, since the area where we have a 180º relationship shifts toward the audience. The farther apart we place them, the more cancellations appear, giving rise to the familiar alleys.
We can conclude that to always have summation and avoid cancellations, we should not separate subwoofers by more than 240º of the highest frequency to be reproduced; in multi-way systems, this frequency is determined by the upper crossover frequency. Obviously, Harry Olson also reached all these conclusions, as the illustrations in his book show.
Subs in a line
Now that we know the maximum relationship we must not exceed, in the same 60x30m venue we had before, we have now set up an example with 8 subwoofers in a line to see whether we can solve the problem. Let's see what happens when we run the prediction at 100Hz. Sure enough, since we have spaced the cabinets 2 m apart, we are still within the 240º limit for the chosen maximum frequency of 100Hz, so there will be summation.
We see that the rule holds for 80Hz, since its wavelength is longer. And it continues to hold for lower frequencies, for example 50Hz.
In enclosed venues, we should place the cabinets nearest the walls at a minimum distance corresponding to 120º of the highest frequency to be reproduced. This is because we have to take into account the phantom image created by the wall, which results in another virtual source located the same distance behind the wall, with the resulting acoustic effect. So by placing the last cabinet at 120º we manage to have 240º of separation from the virtual source.
So it is clear that we will prefer line configurations of subwoofers to a typical L and R configuration.
The only drawbacks we find are that coverage is quite narrow and is limited by the outermost cabinets at each end, and there is also more energy behind the array, which in many cases is a problem.
Subwoofer arc
To avoid the narrow-coverage drawback of the line array, there is another array option that lets us gain coverage at the cost of less pressure at the mix position.
Remember that a cabinet's coverage is determined by the angle formed by the points on either side of the axis where the sound pressure drops 6dB. Let's picture the 8 subwoofers, this time arranged in an arc. To get more coverage depending on the shape of the venue, we need to mark points within the venue at which to aim the bisector of each cabinet, in order to achieve 0º at each point.
Once the prediction is done, we see that we have indeed widened the coverage, although the sound pressure level at the mix position has dropped slightly. But it is always better for the whole audience to have little level difference between areas than for the engineer to be the main beneficiary while a large part of the audience suffers with the "alleys." We have also managed to reduce the pressure level on stage.
There is another way to make the arc: without moving the subwoofers, leaving them in a straight line. This involves calculating the distance along the X axis from the cabinet nearest the mix position (the one that has not been moved) to the adjacent one, and so on, using the center cabinet as the reference.
In our example, these were the results:
Center cabinet 1: x1=10.8
Cabinet 2: x2=10.61
Cabinet 3: x3=10.22
Cabinet 4: x4=9.74
Cabinet 1 delay: Always 0
Cabinet 2 delay: x1-x2/V=0.55ms
Cabinet 3 delay: x1-x3/V=1.7ms
Cabinet 4 delay: x1-x4/V=3.11ms
In this way we have created an electronic arc that simulates the physical arc, also widening coverage and putting less energy on stage. Indeed, the line array, with or without delay simulating the electronic arc, is a configuration used more and more every day, since it allows the most even coverage and shows the least difference between the far field and the near field.
However, the opposite happens to placing the subwoofers in a block: we have a lot of pressure in front of the cabinets and much less in the far field. That is why we get the sense that line arrays reach farther. These arrays are very coherent when combined with line array systems.
Cardioid subwoofers
This surprising theory, already described by Harry Olson, who called it the "END FIRED LINE SOURCE," consists of grouping subwoofers one behind the other to achieve cardioid directivity, with constructive summation at the front and significant cancellation at the rear.
It requires at least 4 subwoofers to cancel 2 octaves. The band from 40Hz to 125Hz is usually chosen, since we are dealing with a subwoofer. It consists of placing subwoofers one in front of another and adding progressive "delay"; with 4 subwoofers, 4 channels of electronic "delay" are needed. The distance between each of the subwoofers (center to center) is what defines the electronic delay value (distance converted to time in milliseconds).
In our case we choose a center frequency of 85Hz, whose wavelength is 4m, as follows from the formula:
Wavelength = V/Fr = 340/85= 4m. If we spaced the cabinets 1m apart, each one would need the corresponding electronic delay added; converting it to time, we get 2.94ms. T= e/V = 1/ 340 = 0.00294s. To convert it to milliseconds we multiply by 1,000 and get the 2.94ms mentioned.
The spacing between the first and second elements defines the center of the upper rear cancellation frequency.
The spacing between the first and third elements defines the center of the second rear cancellation frequency (half of the previous case)
The spacing between the first and fourth elements defines the center of the third rear cancellation frequency (one third of the first case).
For example, to cancel from 30Hz to 125Hz you should do the following:
Subwoofer 1 (0ms delay)
Subwoofer 2 (1m in front of the first, 2.94ms delay)
Subwoofer 3 (2m in front of the first, 5.88ms delay)
Subwoofer 4 (3m in front of the first, 8.82ms delay)
Subwoofer 1 is the first, that is, the one closest to the stage, and subwoofer 4 is the one closest to the audience. Obviously, all the subwoofers must have the same polarity and level, as well as the same order or slope in the HPF and LPF filters. The result is a 12dB summation at the front (due to the use of 4 subwoofers) and more than 20 dB of reduction at the rear.
Let's see what happens when we run the corresponding acoustic predictions, placing 4 subwoofers 1m apart center to center with a progressive delay of 2.94ms. There are other cardioid subwoofer techniques; for example, from the bandwidth you want to cancel, you select the middle frequency, place one subwoofer, and place the second one in front of it, separated (center to center) by a quarter of the wavelength of that frequency; then electronic "delay" is added to the rear subwoofer, and the rear subwoofer's polarity is also inverted.
These cardioid subwoofer techniques are very fashionable and, although Meyer Sound was one of the first to experiment with them, today other brands such as Nexo, d&B and Adamson are following that path.
*Photo: Louise Stickland. WIcreations
Conclusion
We have seen that none of these techniques are new; they are based solely on physics and acoustics written more than half a century ago, but they are being applied today. What we always try to do with these instructional articles is to make these theories and experiences accessible to everyone, so that each of you can choose the array that best suits each case. Remember:
L R system: Creates summation at the mix position and alleys in the audience
Line system: The response is more even and the alleys disappear; narrow coverage and significant level on stage.
Physical arc system: The response remains even; we widen coverage and reduce the level on stage.
Electronic arc system: Identical response to the previous one, with reduced rear level and no need to build a physical arc.
Cardioid sub system: Even response and strong rear cancellation, very clean stage
